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Q: For each of the following integrals, indicate whether integration by substitution or integration by ...

A: Known fact:Integration by parts:When an integral contains the product of two functions, then integra...

Q: The revenue from the sale of a product is, in dollars, R = 1500x + 3000(3x + 3)−1 − 1000 where x i...

A: The revenue from the sale of a product is, in dollars,R = 1500x + 3000(3x + 3)−1 − 1000where x is th...

Q: 8xy′+4(ln x)y)(4) +5x3 y′=−6x4 y−9xy″ What is the order of the differential equation shown above?

A: The given differential equation is, 8xy′ +4(lnx)y4 +5x3y′ = -6x4y - 9xy″.The order of the highest d...

Q: How can I get the result? Which is the result?

A: The given function is,

Q: Using disks or washers, find the volume of the solid obtained by rotating the region bounded by the ...

A: The given curve is y = x^2/3, x=1 and y=0.

Q: Let (0 ifx-5 f(x) 0 ifz 4 and 9(x)-f(t)dt 5 Determine the value of each of the following (d) g(5) (e...

A: The functions are given as

Q: Find the flux of the following vector field across the given surface with the specified orientation....

A: Let r be the vector on the surface of the cylinder y=6x2 for 0 ≤ x ≤ 4, 0 ≤ z ≤ 2.Let's parameter...

Q: Find the derivative of in two ways: first by applying the product rule and second by expanding the p...

A: Applied product rule and found f'(x).

Q: Use any method to determine if the series converges or diverges. Give reasons for your answer.

A: Refer to the question.Here we have to find the convergence of the series,

Q: Use the shell method to find the volume of the solid generated by revolving the region bounded by th...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3.Please resubmit the question and sp...

Q: Find the area of the following surface using a parametric description of the surface. The cap of t...

A: Consider the surface that is the cap of sphere:

Q: Which is the result?

A: The given function is,

Q: During the first four months of employment, the monthly sales S (in thousands of dollars) for a new ...

A: Part (a)S= S(x)= 9 / x + 10 + x / 4, x ≥ 4The given function is defined only for x ≥ 4. We don't hav...

Q: dy If y 22 x, then dx 9.7 1. O 22 0. O 5. N O O O OO

A: The given equation is y=22+x.

Q: Marginal Revenue. Suppose the total revenue function for a blender is R(x)= 36x-0.01x2 dollars where...

A: The total revenue function for a blender is R(x)= 36x-0.01x2 dollars where x is the number of units ...

Q: FIND THE DERIVATIVE OF THE FUNCTIONy=0.6e to the fifth(x) degree

A: The given function "y" is shown on the white board. We need to find its derivative. Before we get in...

Q: How can I get the result? Which is the result?

A: we are given a function as

Q: Calculate the derivative of the function y = (6^6 + 3)^x using the fact that b^x = e^(x ln b) and by...

A: Consider the given function:

Q: a), b) and c) please. I also forgot how to write interval notation....

A: To find the direction we have to graph the function v(t)= 3t^2-36t+105 ; [0,8]. And then we check th...

Q: Which of the following is the power series representation for f(10x)? O A. B. 10k co (1-(10x*) In k ...

A: The power series representation for f(10x) is,

Q: Find the area of the region that lies inside both curves. r = 9 + cos(θ), r = 9 − cos(θ)

A: To calculate the area of the given region (by integration) described by polar coordinates

Q: Need solution to 1b.

A: Part 1b.In this question, we have a function for which we have to solve limits, function is given be...

Q: Determine the interval(s) on which the following function is continuous, then analyze the given limi...

A: (2+2cosx) and sinx both are continuous functions. So the function (2+2cos x)/sinx will be discontinu...

Q: Use the substitution formula Integral from a to b f left parenthesis g left parenthesis x right pare...

A: Obtain the value of the integral as follows.

Q: Find the point on the plane 4x+5y+x=11 that is nearest to (2,0,1). What are the values for x, y, and...

A: The equation of the plane is

Q: How do you solve the limit of this graph?

A: x->-1^- means x is slightly less than -1.

Q: How can I do this? Which is the result?

A: Given:The function is

Q: a) and b) please

A: Part (a)The population of the town in 2016 is 63,000 and the growth rate is 2.3% per year.

Q: find the volume aquired by taking by region bound by y=x^2 and y=x^4 and rotating it around x=-1

A: To calculate the volume bounded by the curve y=x2 and y=x4 which is rotating about the line x=-1. No...

Q: Find the area, in square units, bounded by f(x)=3x+5 and g(x)=2x+1 over the interval [0,12]. Do not ...

A: Area of region between f(x) and g(x) over the interval [0,12] is computed as follows.

Q: Determine if y=e2x −x+1 is a solution to y′−2x=−3+2y.

A: The given differential equation is y′−2x=−3+2y.The solution of the deferential equation is given as...

Q: Hello, I need help explaining how pi(k)/2 came about, I know where pi/4 came from. Thank you for th...

A: Consider the provided trigonometry equation.

Q: how to find Find the exact length of the polar curve. r = θ2, 0 ≤ θ ≤ 7π/4

A: The polar curve I given as, r = θ2, 0 ≤ θ ≤ 7π/4.The formula to calculate the exact length of th...

Q: Suppose that the rate at which the concentration of a drug in the blood changes with respect to time...

A: Given:The rate of change of concentration of a drug in blood with respect to time t is

Q: The rate at which blood pressure decreases in the aorta of a normal adult after a hearbeat is dp/dt=...

A: It is given that rate at which the blood pressure decreases in the normal adult is dp/dt=–46.645e–0....

Q: (2x-3)4 dx 10

A: Given:The integral is

Q: If the formula describing the distance s(in feet) an object travels as a function of time(in seconds...

A: The distance s(in feet) an object travels as a function is s = 100 + 160 t -16t2.It is known that, t...

Q: Write the iterated integral for a sphere centered at (0,0,0) with a radius of 2. Use the order dz dx...

A: From the given the sphere equation is x2+y2+z2=22.

Q: The equation abs(y/a)^n + abs(x/a)^n = 1, where n and a are positive real numbers. Make a complete ...

A: The equation abs(y/a)^n + abs(x/a)^n = 1,

Q: a. Write the equation of the line that represents the linear approximation to the following function...

A: We have to find f'(x) first.

Q: b. Find the area of the region bounded by Y = xe ax and the x-axis on the interval 0,41, where a> 0....

A: Area of region which is bounded by f(x) and x-axis on [0,4] computed as follows.

Q: Find the absolute extrema of the given function on the indicated closed and bounded set R. (Order yo...

A: We are given a function and a closed interval as

Q: Activity 5 Inverse Functions and their Derivatives 10. When a camera flash goes off, the batteries i...

A: Given:The function is Q(t) = Q0(1−e−t/a), where t is the time in seconds and Q0 is the maximum char...

Q: What is the particular solution for y′=5ex −6x3 +4x such that y(0)=−8? Do not include "y=" in your a...

A: The given differential equation is, y′=5ex −6x3 +4x.

Q: Do the domain of the following function:

A: Consider the provided function.

Q: Calculate the directional derivative in the direction of v at the given point. fx, v)- tan Cy). -(1,...

A: The partial derivatives of f(x,y) at the point (x,y)=(5,2)are:

Q: Find y' if x^y = y^x .

A: Given,

Q: Find the slope of the secant line between x=2 and x=5 on the graph of the function f(x)=−2x2+2x+3.

A: We have to find the slope of the secant line between x=2 and x=5 on the graph of the function f(x)....

Q: Find the intervals on which f is increasing and the intervals on which it is decreasing f(x) = -2 ...

A: First, we find f'(x).

Q: y′=−3x+9 Determine the particular solution to the differential equation that passes through the poin...

A: The given differential equation is y’ = –3x+9.